I have spent 3 hours with a family member who has 40+ years of chemistry teaching experience and he and I cannot seem to solve the following problem:

A 5.69 g sample of iron metal was heated in boiling water to 99.8 C. Then it was dropped into a beaker containing 100.0 g of H2O at 22.6 C. Assuming that the water gained all of the heat lost by the iron, what is the final temperature of the H2O and Fe?


Let me know if anyone can help me understand how to solve. Thanks!

I'm really surprised that someone with +40 years of experience in chemistry cannot solve this chemistry proble while it involves one of the fundamental laws of science; energy cannot be created nor destroyed, but only converted to other forms...

Let the final temperature of the water and iron be T. The amount of heat lost by the iron will be given by:

Q = -mc\Delta T = -(5.69)c_{Fe}(T-99.8)

The amount of hear gained by the water is given by:

Q = mc\Delta T = (100)c_{H_2O}(T-22.6)

Equate both.

c_Fe = 0.45 J/(gK)
c_H2O = 2.08 J/(gK)